Optics Figures - Figure 5,6

Figure 5 - Physiological optics

Physiological optics. The images represent the human point spread function (PSF), measured at different wavelengths and visual field positions. The blue lines are the corresponding vertical line spread function (LSF) computed by summing the PSF down the columns. (a) Comparisons at different wavelengths for subject 1 in the fovea. (b) Comparison at different eccentricities for subject 4 at 550 nm. (c) Comparisons of three subjects at 550 nm and 5◦ eccentricity. The PSFs and LSFs were calculated using ISETBio with data from [Jaeken and Artal, 2012].
zCoeffDatabase = 'Artal2012';
eyeside = 'right';
pupilDiamMM = 3.0;
centerpsf = true;
wave = 400:10:700;

Top row

Vary wavelength.
params.wave = [450 550 650];
params.thisSubject = 1;
params.positionDegs =[0 0];
for thisW = params.wave
thisSubject = params.thisSubject;
positionDegs = params.positionDegs;
[oi, psf, support, zCoeffs, subjID] = ...
oiPosition(zCoeffDatabase, 'position',positionDegs, ...
'pupil diameter', pupilDiamMM, 'subject rank', thisSubject, ...
'wave',wave, ...
'eye side', eyeside,'center psf',centerpsf);
idx = find(wave == thisW);
ieNewGraphWin;
imagesc(support.x,support.y,psf(:,:,idx)/max2(psf(:,:,idx)));
axis image; mp = parula(256); mp(1:4,:) = repmat([0.5 0.5 0.5],[4,1]);
colormap(mp);
tMarks = (-15:5:15); mn = -10; mx = 10;
set(gca,'xtick',tMarks,'xlim',[mn mx],'ylim',[mn mx]);
set(gca,'ytick',tMarks);
grid on; hold on; axis xy
% Superimpose the line spread
lsf = psf2lsf(psf);
lsf = lsf/sum(lsf(:));
% Plot the LSF starting from -10 and scaled to -5.
thisLSF = lsf(:,idx)/max(lsf(:,idx));
plot(support.y,5*thisLSF-10,'b-','Linewidth',4);
title(sprintf('W %d Sub %d',thisW,thisSubject));
set(gca,'FontSize',20);
xlabel('Position (arc min)'); ylabel('Position (arc min)');
end
Subject 49 from right eye requires central refraction correction
Subject 49 from right eye requires central refraction correction
Subject 49 from right eye requires central refraction correction

Second row

Vary visual field position
zCoeffDatabase = 'Artal2012';
params.wave = 550;
params.thisSubject = 4;
params.positionDegs =[1 0; 10 0; 20 0];
for ii = 1:3
positionDegs = params.positionDegs(ii,:);
thisW = params.wave;
thisSubject = params.thisSubject;
[oi, psf, support, zCoeffs, subjID] = ...
oiPosition(zCoeffDatabase, 'position',positionDegs, ...
'pupil diameter', pupilDiamMM, 'subject rank', thisSubject, ...
'wave',wave, ...
'eye side', eyeside,'center psf',centerpsf);
idx = find(wave == thisW);
ieNewGraphWin;
imagesc(support.x,support.y,psf(:,:,idx)/max2(psf(:,:,idx)));
axis image; colormap(mp);
tMarks = (-15:5:15); mn = -10; mx = 10;
set(gca,'xtick',tMarks,'xlim',[mn mx],'ylim',[mn mx]);
set(gca,'ytick',tMarks);
grid on; axis xy; hold on;
lsf = psf2lsf(psf);
lsf = lsf/sum(lsf(:));
thisLSF = lsf(:,idx)/max(lsf(:,idx));
plot(support.y,5*thisLSF-10,'b-','Linewidth',4);
title(sprintf('W %d Sub %d Pos %f',thisW,thisSubject,positionDegs(1)));
set(gca,'FontSize',20);
xlabel('Position (arc min)');
if ii == 1, ylabel('Position (arc min)'); end
end

Third row

Compare subjects
zCoeffDatabase = 'Artal2012';
params.wave = 550;
params.thisSubject = [5 15 25];
params.positionDegs =[5 0];
for ii = 1:3
positionDegs = params.positionDegs;
thisW = params.wave;
thisSubject = params.thisSubject(ii);
[oi, psf, support, zCoeffs, subjID] = ...
oiPosition(zCoeffDatabase, 'position',positionDegs, ...
'pupil diameter', pupilDiamMM, 'subject rank', thisSubject, ...
'wave',wave, ...
'eye side', eyeside,'center psf',centerpsf);
idx = find(wave == thisW);
ieNewGraphWin;
imagesc(support.x,support.y,psf(:,:,idx)/max2(psf(:,:,idx)));
axis image; colormap(mp);
tMarks = (-15:5:15); mn = -10; mx = 10;
set(gca,'xtick',tMarks,'xlim',[mn mx],'ylim',[mn mx]);
set(gca,'ytick',tMarks);
grid on; axis xy; hold on;
lsf = psf2lsf(psf);
lsf = lsf/sum(lsf(:));
thisLSF = lsf(:,idx)/max(lsf(:,idx));
plot(support.y,5*thisLSF-10,'b-','Linewidth',4);
set(gca,'FontSize',20);
xlabel('Position (arc min)');
if ii == 1, ylabel('Position (arc min)'); end
title(sprintf('W %d Sub %d Pos %f',thisW,thisSubject,positionDegs(1)));
end
Subject 51 from right eye requires central refraction correction
Subject 11 from right eye requires central refraction correction
h = colorbar;

Figure 6 - Optical shift-invariance.

Optical shift-invariance. We assess the importance of the optical blur by calculating its impact on the responses in a cone mosaic. In this example, we compare the edge-spread function (ESF) of an edge at three different eccentricities. (a) First we synthesize a typical cone mosaic near 1 deg eccentricity. (b) Then, we compute the number of excitations in each cone in response to a sharp edge (broad spectrum, 5 ms exposure). (c-e) Using wavefront measurements from three different subjects, we compute the L-cone excitations in this mosaic. Each panel is for a different subject. Within each panel we compare the ESF using wavefront data measured at 1◦, 5◦ and 10◦. For two subjects (c,e), the ESF is the same at these eccentricities. For one subject (d) the the edge spread changes with eccentricity. Wavefront data from ISETBio subjects 15, 49 and 51, measured by [Jaeken and Artal, 2012]. The ISETBio script for this figure makes this comparison for many other subjects and stimuli.

Create the stimulus and cone mosaic

scene = sceneCreate('slanted edge', 512, Inf);
scene = sceneSet(scene,'fov',2);
sceneWindow(scene);
cmP = cMosaicParams;
cmP.positionDegs = [1,0];
cmP.sizeDegs = [0.5 0.3];
cm = cMosaic(cmP);
min cone aperture diameter = 2.566750 microns
cm.integrationTime = 0.05;
cm.visualize;

Loop on subjects and eccentricities

zCoeffDatabase = 'Artal2012';
eyeside = 'right';
pupilDiamMM = 3.0;
centerpsf = true;
wave = 400:10:700;
ecc = 1; % [1, 5, 10];
subjectRank = 15; % [10, 40];
hdl = ieNewGraphWin;
for ss = 1:numel(subjectRank)
n = 0;
uData = cell(numel(ecc),1);
for ii = ecc
n = n + 1;
positionDegs = [ii 0];
[oi, psf, support, zCoeffs, subjID] = ...
oiPosition(zCoeffDatabase, 'position',positionDegs, ...
'pupil diameter', pupilDiamMM, 'subject rank', subjectRank(ss), ...
'wave',wave, ...
'eye side', eyeside,'center psf',centerpsf);
% These are the pupilMM and zCoeffs from the top of the file.
% oi = oiCreate('wvf human', pupilMM, zCoeffs, wave);
oi = oiCompute(oi,scene);
% oiWindow(oi);
cm.compute(oi);
allE = cm.compute(oi);
[uData{n}, hdl] = cm.plot('excitations horizontal line',allE,...
'ydeg',0, ...
'plot title',sprintf('Optics ecc %d Rank %d',ii,subjectRank), ...
'hdl',hdl);
cm.plot('excitations',allE);
end
end
Subject 11 from right eye requires central refraction correction
min cone aperture diameter = 2.576892 microns

Plot the curves for the L-cones

ieNewGraphWin;
cc = 1; % Which color channel
sym = {'ko-','kx:','ks-'};
for ii=1:numel(ecc)
posE = uData{ii}.pos;
roiE = uData{ii}.roiE;
tmp = squeeze(roiE{cc});
mn = mean(tmp(:));
mx = max(tmp(:));
plot(posE{cc}, (tmp)/mx,sym{ii},'LineWidth',2);
hold on;
end
legend({num2str(ecc')},'Location','northwest');
grid on;
title(sprintf('Subject %d Conetype %d',subjectRank(ss),cc));
xlabel('Position (deg)'); ylabel('Relative excitations');
set(gca,'fontsize',18)
set(gcf,'Position',[4.0000e-04 0.5486 0.7992 0.3687]);
%% Make a test scene
params = harmonicP;
params.freq = 80;
params.row = 1024; params.col = 1024;
scene = sceneCreate('harmonic',params);
scene = sceneSet(scene,'fov',10);
sceneWindow(scene);
zCoeffDatabase = 'Artal2012';
subjectRank = 1; % 1:8; % [2, 5, 10, 20];
eyeside = 'right';
pupilDiamMM = 3.0;
centerpsf = true;
wave = 400:10:700;
pos = -3:1:3;
for thisSubject = subjectRank
lsf = zeros(201,numel(wave),numel(pos));
for ii=1:numel(pos)
positionDegs = [pos(ii) 0]; % v
[oi, psf, support, zCoeffs, subjID] = ...
oiPosition(zCoeffDatabase, 'position',positionDegs, ...
'pupil diameter', pupilDiamMM, 'subject rank', thisSubject, ...
'wave',wave, ...
'eye side', eyeside,'center psf',centerpsf);
% x, w, pos
lsf(:,:,ii) = psf2lsf(psf);
end
% Find the luminance weighted sum (luminance)
lumLSF = zeros(201,numel(pos));
vLambda = ieReadSpectra('Vlambda',wave);
for ii=1:numel(pos)
lumLSF(:,ii) = lsf(:,:,ii)*vLambda(:);
end
lumLSF = lumLSF/max(lumLSF(:));
% Show as line plots
ieNewGraphWin;
hold on;
for ii=1:2:numel(pos)
if abs(pos(ii)) <= 4
plot(support.y,lumLSF(:,ii),'k-','Linewidth',2);
end
end
grid on;
xlabel('Arc min'); ylabel('Relative luminance')
set(gca,'ylim',[-0.1 1]); set(gca,'xlim',[-5 5]);
set(gca,'xtick',(-5:2.5:5));
legend(sprintf('Subject %d',thisSubject));
drawnow; pause(0.5);
print(sprintf('LSF_%s_%d',zCoeffDatabase,thisSubject),'-dpng');
end
Subject 49 from right eye requires central refraction correction Subject 49 from right eye requires central refraction correction Subject 49 from right eye requires central refraction correction Subject 49 from right eye requires central refraction correction Subject 49 from right eye requires central refraction correction Subject 49 from right eye requires central refraction correction Subject 49 from right eye requires central refraction correction

Show LSF at multiple waves

wavesamples = [400, 450, 500, 550, 600, 650];
leg = cell(numel(wavesamples),1);
for ii=1:numel(wavesamples)
leg{ii} = [num2str(wavesamples(ii)),' nm'];
end
ieNewGraphWin;
hold on;
for ii=1:numel(wavesamples)
idx = find(wave == wavesamples(ii));
plot(support.y,lsf(:,idx)/max(lsf(:,idx)),'Linewidth',2);
end
set(gca,'xlim',[-8 8],'ylim',[0 1]);
legend(leg);
xlabel('Arc min'); ylabel('Relative intensity');
grid on;

Show a surface view of the linespreads

ieNewGraphWin;
lsfs = zeros(201,numel(pos));
for ii=1:numel(pos)
tmp = squeeze(lsf(:,idx,ii));
thisLSF = lsf(:,idx,ii)/sum(lsf(:,idx,ii));
lsfs(:,ii) = thisLSF;
end
%% Show as a surface
surf(pos,support.y,lumLSF);
xlabel('Eccentricity (deg)'); ylabel('Arc min');
set(gca,'ylim',[-5 5]);
title(sprintf('Artal data, Subj rank: %d',subjectRank));
% Compare at a single wavelength
thisWave = 450;
idx = find(wave == thisWave);
lsfs = zeros(201,numel(pos));
for ii=1:numel(pos)
tmp = squeeze(lsf(:,idx,ii));
thisLSF = lsf(:,idx,ii)/sum(lsf(:,idx,ii));
lsfs(:,ii) = thisLSF;
end
%{
ieNewGraphWin;
hold on;
for ii=1:numel(pos)
plot(support.x,lsfs(:,ii));
end
%}
%% Highest resolution
ieNewGraphWin;
surf(pos,support.y,lsfs);
xlabel('Eccentricity (deg)'); ylabel('Arc min');
colormap(cool);
title(sprintf('Wave %d',thisWave));
%% Sampled at 0.5 min which is the cone density in the fovea
possamples = (0:1:10);
% arcmin = support.y(:);
% possamples = pos;
arcmin = (-10:0.5:10)';
lsfsInterp = interp2(pos(:),support.y(:),lsfs,possamples,arcmin);
ieNewGraphWin;
surf(possamples,arcmin,lsfsInterp);
xlabel('Eccentricity (deg)'); ylabel('Arc min');
title(sprintf('Wave %d',thisWave));
%%
%{
surf(possamples',arcmin(:),sInterp);
xlabel('Eccentricity (deg)'); ylabel('Arc min');
colormap(cool);
%}
%%
%{
xlabel('arc min'); ylabel('relative intensity');
imagesc(support.x, support.y, squeeze(psf(:,:,idx)));
axis 'square'; colormap(gray); xlabel('arc min'); ylabel('arc min');
%}
%% Try putting the zCoeffs for a subject into an oi